Efficient evaluation of Pauli strings with entangled measurements
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Abstract
The advent of cloud quantum computing accelerates development of quantum algorithms. In particular, it is essential to study variational quantum-classical hybrid algorithms, which are executable on Noisy Intermediate-Scale Quantum (NISQ) computers. Evaluations of observables appear frequently in the variational quantum-classical hybrid algorithms for NISQ computers. By speeding up the evaluation of observables, we can realize a faster algorithm and save resources of quantum computers. The grouping of observables with separable measurements has been conventionally used, and the grouping with entangled measurements has also been proposed recently by several teams. In this paper, we demonstrate that entangled measurements enhance the efficiency of evaluation of observables both theoretically and experimentally by taking into account the covariance effect, which may affect the quality of evaluations of observables. We also propose using a part of entangled measurements for grouping in order to keep the depth of extra gates constant. Our proposed method is expected to be used in conjunction with other related studies. We hope that entangled measurements become crucial resources not only for joint measurements but also quantum information processing.